Software　reliability　is　an　important　attribute　of　software　quality.　To　achieve　higher　reliability,　software　development　must　include　a　testing　phase　in　which　faults　can　be　detected　and　corrected.　The　software　reliability　growth　model　(SRGM)　has　evolved　from　modeling　merely　the　fault　detection　process　(FDP)　into　incorporating　the　fault　correction　process　(FCP)　as　well.　However,　restricted　by　mathematical　tractability,　it　is　difficult　to　incorporate　into　analytical　models　with　more　complicated　factors,　such　as　the　dependency　between　faults　and　the　influence　of　staffing　levels.　This　limits　the　application　of　analytical　models.　Therefore,　it　is　promising　to　adopt　data-driven　methods　such　as　the　artificial　neural　network　(ANN)　to　model　the　FDP　and　the　FCP　as　no　specific　assumptions　are　needed.　In　this　study,　a　stepwise　prediction　model　is　proposed　to　model　the　FDP　and　the　FCP　based　on　the　ANN.　Testing　effort　is　considered　in　our　model　since　it　has　a　great　influence　on　fault　detection　and　correction　process.　Using　real　data,　the　performance　of　different　types　of　neural　networks　are　compared　with　the　analytical　model.　The　empirical　study　has　confirmed　the　effectiveness　of　the　proposed　models.　Further,　the　optimal　policy　of　the　software　release　time　is　also　presented　to　illustrate　the　applications.　(c)　2020　Elsevier　B.V.　All　rights　reserved.